I haven't used bike pumps in those conditions, but I am a cell phone tower climber, and I've worked at heights in subfreezing conditions. When we have items that need to be warmed up before use, or can be damaged by freezing, we put them inside our clothing, next to our base layer. Whatever pump you get, I would recommend that if you get a flat, the first thing you should do is put the pump, tube, and any other tools inside your clothes to warm them up. Take each out as you need it, and replace as soon as possible.
It's not comfy, but it works.